A communication system typically includes a transmitter (TX), a receiver (RX) and a lossy transmission channel. For example, FIG. 1 shows exemplary communication system 100 including transmitter 102, receiver 106, and channel 104. During normal operation, transmitter 102 typically encodes data to be transmitted into symbols and sends the encoded symbols through channel 104. Receiver 106 typically receives the encoded symbols from channel 104 and decodes the symbols.
The symbols may be encoded in many different ways. For example, pulse-amplitude modulation (PAM) may be used. An example of PAM having two levels (PAM-2) is non-return to zero (NRZ) modulation. NRZ is a binary code that typically represents a one by a positive voltage and a zero by a negative voltage.
To decode symbols transmitted using PAM-2, a binary data slicer is typically used. A data slicer, also known as a slicer, is a circuit that samples an analog signal (e.g., a symbol) and determines its logical value. In other words, it generates a digital signal based on the sampled analog signal. For example, a data slicer for decoding symbols generated using NRZ modulation may be implemented with a comparator that outputs 1 when the input is positive and 0 when the input is negative.
As shown in FIG. 1a, signal Sout received by receiver 106 may be different than signal Sin transmitted by transmitter 102. In other words, the finite bandwidth and reflections of channel 104 may modify signals as they go through the channel. Such modifications may cause the receiver to incorrectly decode the received symbols, thereby leading to higher bit error rates in the communication system.
FIGS. 1b and 1c show graphs of signals Sin and Sout, respectively. FIG. 1b shows a pulse being transmitted by transmitter 102 at time t0. FIG. 1c shows the signal being received by receiver 106 at time t0. As shown in FIG. 1c, signal Sout may be modified by channel 104. FIG. 1c may be understood as the channel pulse response (the convolution between a single pulse and the channel impulse response). In other words, coefficients C−1, C0, C1, C2, C3, C4, C5, etc. may be understood as channel pulse response coefficients. For the sake of simplicity, the transmission line delay that may be associated with channel 104 has been ignored.
As shown in FIG. 1c, transmitting a symbol at time t0 through channel 104 may affect subsequently received symbols through channel 104 at times t1, t2, t3, t4, t5, etc. Such interference between symbols is known as inter-symbol interference (ISI). Interference associated with subsequent symbols is known as post-cursor ISI.
To reduce ISI, a receiver typically uses an equalizer such as a continuous linear equalizer (CTLE) followed by a decision feedback equalizer (DFE). The CTLE is designed to match the channels inverse transfer function. A DFE is a non-linear equalizer that uses the information from the CTLE together with detected symbols to produce an estimate of the post-cursor ISI. Such estimate is subtracted from the output to cancel ISI. FIG. 1d shows an exemplary implementation of receiver 106. Receiver 106 includes CTLE 112 and DFE 114. Variable gain amplifier (VGA) 110 may be used to adjust the amplitude of the incoming signal to optimize the dynamic range and avoid saturation.
Other modulation techniques may also be used in a communication system. For example, several standard bodies adopt multi-level modulation instead of PAM-2. For example, PAM-4 (4-level pulse amplitude modulation) has been adopted by the IEEE 802.3bs standard and the OIF CEI-56G standard. PAM-4 is a modulation technique that doubles the data rate while having the same bandwidth requirements than PAM-2. PAM-4 achieves four levels by dividing the vertical eye diagram with three thresholds. PAM-4, therefore, generates 2 bits of data per symbol received.